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A035080 Number of asymmetric connected graphs where every block is a complete graph.

%I A035080 #19 Feb 19 2016 05:51:11
%S A035080 1,1,0,0,0,0,1,3,7,21,60,168,472,1344,3843,11104,32305,94734,279708,
%T A035080 831401,2485877,7474667,22589771,68594611,209198103,640591332,
%U A035080 1968920180,6072766832,18791062733,58321579888,181524367875,566488767763,1772261945866,5557515157647
%N A035080 Number of asymmetric connected graphs where every block is a complete graph.
%H A035080 Alois P. Heinz, <a href="/A035080/b035080.txt">Table of n, a(n) for n = 0..600</a>
%F A035080 G.f.: A(x) = B(x) + C(x) - B(x)*C(x), where B and C are g.f.s of A007561 and A035079, respectively.
%F A035080 a(n) ~ c * d^n / n^(5/2), where d = 3.38201646602027280742981874... (same as for A007561), c = 0.12430588691278777480105... . - _Vaclav Kotesovec_, Sep 10 2014
%p A035080 g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A035080       add(binomial(b((i-1)$2), j)*g(n-i*j, i-1), j=0..n/i)))
%p A035080     end:
%p A035080 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A035080       add(binomial(g(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
%p A035080     end:
%p A035080 a:= n-> b((n-1)$2)+g(n$2)-add(b((i-1)$2)*g((n-i)$2), i=0..n):
%p A035080 seq(a(n), n=0..40); # _Alois P. Heinz_, May 20 2013
%t A035080 g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[b[i-1, i-1], j]*g[n-i*j, i-1], {j, 0, n/i}]]]; b[n_, i_] := b[n, i] = If[n==0, 1, If[i < 1, 0, Sum[Binomial[g[i, i], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n-1, n-1] + g[n, n] - Sum[b[i-1, i-1]*g[n-i, n-i], {i, 0, n}]; Table[ a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 19 2016, after _Alois P. Heinz_ *)
%Y A035080 Cf. A007561, A035081.
%K A035080 nonn
%O A035080 0,8
%A A035080 _Christian G. Bower_, Nov 15 1998